Note: This article has been edited to include suggestions from the comments, particularly to look only at the Texas sample and account for the Texas park/pitchers effect.

Today was not a good day for Alex Rodriguez. After news broke earlier this year that he had tested positive for steroids in 2003, A-Rod tried desperately to regain some respect and trust by admitting not only to one-time use, but by opening up and putting it all on the table: three years worth of juicing that no one would have known about if not for his candor. Now, reports of use dating possibly back to high school and continuing past 2003 into his years with the Yankees have leaked, and regardless of how accurate these reports turn out to be, this news shatters a lot of the tenuous trust fans may have reluctantly given. But there are more, and potentially just as damaging, allegations to these reports than that.

The reports allege that A-Rod tipped opposing hitters to what pitches were coming in lopsided games when he was at shortstop with the expectation that those hitters would return the favour when he came up to bat. The steroid allegations are one thing. A lot of people were already convinced his use was not limited to when he admitted using, and to a lot of people, his use at all, let alone for 3 years, is already damning enough on that front. But this adds a few new barrels of kerosene for fans to throw on the proverbial fire. For a guy who already has a reputation as a selfish ass and a bad teammate, can there be much worse than news of deliberately selling out teammates to the opposing team under the small chance that they might in turn help him pad his stats a bit in a meaningless game?

Needless to say, his many detractors will likely run wild with this. However, that's not what we're here to do. There will be enough of that. What I want to look at is whether we can find any evidence of these new allegations. Unlike trying to find evidence in the numbers of steroid use, this accusation calls for a fairly straightforward approach. All we have to do is look at how batters A-Rod might have tipped hit in lopsided games with A-Rod at short, and compare that to how they would have been expected to hit.

First, we have to determine what hitters we want to look at. Based on the reports, they should be hitters who would have a chance to tip A-Rod back when he is at the plate, so we're talking about other middle infielders. This could also potentially include center fielders, but for now, let's stick with what we can be sure of and see what our sample looks like.

Next, we need to define what situations we want to look at that we would consider lopsided enough for A-Rod to consistently do this. I arbitrarily picked 2 different situations that I felt were sufficiently lopsided that if A-Rod were indeed tipping pitches, it should show up, but were common enough that I would still have a good sized sample to evaluate. One was any game that was at least 7 runs apart in either direction (either with A-Rod's team up or down). The other was any game in the 7th inning or later that was at least 5 runs apart.

Now that we have defined what we want to look at, it's on to the study. I looked at every time a middle infielder was at bat with A-Rod at short in one of these two situations and summed the results to get an aggregate line of what these hitters hit in each situation. Then, to determine what kind of numbers we should expect under normal circumstances, I looked at what the same hitters would have hit in the same number of plate appearances based on their numbers for that season as a whole. For example, in 1998, Chuck Knoblauch came to the plate 6 times with A-Rod at short and the score at least 7 runs apart, so I took what he hit in those 6 plate appearances and added them into the group of hitters with A-Rod at short, and then I took what he hit over the 1998 season as a whole, weighted it to 6 plate appearances, and added that into the group establishing what those hitters would be expected to hit. This was done for every middle infielder who batted in a lopsided game with A-Rod at short.

This left me with a total of 693 plate appearances in the first situation and 859 in the second. Both of these are right around or above a full season's worth of PA's for a player, so we're talking about a decent if not ideal sized sample. Here are the results, with the first row showing what the group was expected to hit and the second row showing what they did hit with A-Rod supposedly tipping pitches:

7+ Run Games

AVG

SLG

OBP

OPS

Season

.268

.394

.329

.723

w/ A-Rod

.281

.422

.333

.755

5+ Run Games, 7th inning or later

AVG

SLG

OBP

OPS

Season

.267

.392

.327

.719

w/ A-Rod

.288

.452

.341

.793

Seventy OPS points is a lot. But guess what? That might not be all. I ran the above study again, but this time I left out plate appearances where a runner was on second. Since most batteries work out a series of signs that changes throughout a game to stop the runner on second from stealing and relaying signs to the hitter, there is a good chance A-Rod couldn't read them either in these PAs. Doing this dropped our samples to 551 and 695 PAs, but our lopsided-and-late sample is still a full season's worth. Here are the new results:

7+ Run Games

AVG

SLG

OBP

OPS

Season

.268

.392

.328

.720

w/ A-Rod

.284

.440

.334

.774

5+ Run Games, 7th inning or later

AVG

SLG

OBP

OPS

Season

.267

.391

.327

.718

w/ A-Rod

.295

.472

.340

.812

Whoa. That looks like pretty damning evidence right there. Hitters all of a sudden picked up close to .100 OPS points late in lopsided games with A-Rod at short. We aren't quite ready to say for sure, though, because it's possible batters should hit better in these situations. For example, hitters might hit better in lopsided games. I used the same method to look at how middle infielders hit with anyone besides A-Rod at short in lopsided games compared to how they usually hit. This time, since I'm already dealing with a much larger sample (20-30 thousand PAs), I limited my data to the years 2000 on. Middle infielders hit about the same (-.002 OPS points) in 7+ run games and a fair bit worse (-.023 OPS points) in 5+ run games in at least the 7th inning. If we look at all hitters and not just middle infielders, the results are pretty much the same.

We should also consider that some of these PAs are taking place in Texas and against Texas pitching, where hitters generally do hit better. The majority of the PAs in the sample are in Seattle, where hitters hit a bit worse than average, so the Texas skew should probably not be enough to bring the whole sample up over .100 points compared to what those hitters would normally hit late in lopsided games. There was some interest in the comments in seeing specifically how much of the effect could be explained simply by the Texas skew, however, so we can look only at the Texas games and see if middle infielders benefit more than other hitters late in lopsided games (as I have done in the comments below-see comments for more details). As expected, both middle infielders and non-middle-infielders hit significantly better late in lopsided games against Texas than they normally hit (because they were hitting against, and often in, Texas), but the middle infielders improved far more than the non-middle-infielders. They improved by about .150 OPS points more than the non-MI group, which is even more than the improvement over the control sample we saw above in A-Rod's career sample at short without accounting for Texas.

That the increase is greater in Texas makes sense with the story, since that is where A-Rod has been accused of tipping pitches. He may or may not have been tipping pitches in Seattle as well, or he may have been tipping pitches only in his later years in Seattle. However, we still want to include them in this sample even though we suspect he may not have been tipping pitches there because, if nothing else, it's a simple way to regress the Texas sample. Looking at only the late-and-lopsided PAs in Texas gives us only 227 PAs, so we can't take the numbers at face value. Adding in the Seattle PAs gets us up to a full season's worth and greatly increases our confidence that the increase we are seeing is real.

All considered, that's close .100 points in OPS, in a full season's worth of PAs, that these hitters gained from having A-Rod in the field late in lopsided games. They basically morphed from Joel Youngblood into Dave Parker at the plate. Or from Adam Kennedy into Miguel Tejada. Notice especially the huge jumps in SLG: these hitters were flat out clobbering the ball like they knew what was coming. It's not like those pitchers in Texas needed any extra help without "Crash" Rodriguez screwing with their ERAs either. I hate to say it, but it appears from these numbers that something was up.

But hey, at least he never told someone to drill a bull in the head with a fastball. That we know of, anyway.

30
comments:

Ok, I have no reason left to respect the guy. I hate that, because I really did like him. Watch, over time Bonds is going to become a more publicly sympathetic character, while A Rod becomes a total fool.

I feel the same. I've always felt some need to defend him to an extent. People complained about how horrible he was for signing big contracts when that's what teams decided he was worth, like he should turn them down and say I want to play for less than I'm worth. People called him a greedy jerk for opting out of his contract: that was one of the negotiated clauses the Yankees gave him in exchange for other points in the contract. Teams exercise their own built in opt out clauses all the time in buying out club options. Yet A-Rod is the jerk. People who have never been in a clubhouse with him assume he's a terrible teammate and that everyone must hate him. They talk about how he chokes in the clutch despite his being an undeniably great hitter who has come through in many clutch moments by virtue of his superior hitting skills. It was like people wanted to hate him no matter what he did, and fans weren't above making up reasons to hate him. Even after it came out that he took steroids, it wasn't as clear cut for me, and people were still making up things to throw at him and nailing him for things that were completely irrelevant.

As one of the first truly great players I grew up following from his first day up as a teenager, it's hard for me not to have rooted for and liked the guy. But even beyond that, it got to the point that the people hating him got so ridiculous, and whether you stood up for him or not, if you even pointed out that some of the outlandish things being said were uncalled for, you got bashed mercilessly. It was so distasteful to be in the crowd that hated him that I never really wanted to bother getting upset about him. But now this. I just can't stomach defending the guy's character anymore. I've long since started to see Bonds as less than pure villain as a more complex figure deserving, in some ways of sympathy. I've come to feel that way about McGwire. This is just making it that much harder to feel that way about A-Rod, even after I was already inclined that way from the start with him. It also goes with other isolated incidents, like his calling a pop-up running the bases (and then denying it like it wasn't on tape in HD) or his swiping the ball out of Bronson Arroyo's glove in the playoffs, but this type of systematic crap, and against his own teammates this time, is just a new level. I've never even heard of this.

One minor note, I saw today that I left HBP out of part of my code, so I'm updating the figures now. The only thing it will affect is the OBP (and the OPS, obviously) of the full season samples. Everything else remains the same.

1.) Would you mind giving us the names of the hitters who benefited the most,according to your statistics? After all, if, as you are suggesting, A-Rod tipped off opposing players, it would be good to know who these co-conspirators, such as they are, actually are.

2.) I did my own numbers on Alex, courtesy of stats from baseballmusings.com. His numbers, for the most part, were actually worse in blowout games than better.

You dont control for Texas!! Go look at the Texas ‘ pitching staff OPS against for that season- its .856. Basically, you proved the opposite point- players actually did worse against the Rangers late in blowout games than they did normally. You also ignored the selection bias- the pitchers throwing at that point are likely to be the dregs of MLB. Mop up work for the worst pitching team in baseball? Pretty sure you need to correct for that.

pointing out texas' staff ops doesn't really refute anything here, especially when you consider this study is dealing exclusively with middle infielders. i'm willing to bet that their ops against middle infielders isn't as gaudy as their overall ops.

there are also flaws in pointing out that a-rod's numbers "were actually worse" in blow-out games, namely the fact that you're accounting for his stats for the entire game. this study only accounts for at bats that occurred in games with either a 7 run differential or a 5 run differential in the 7th inning or later. it's no surprise that a-rod's numbers were much worse in games where his team was trailing by 5 runs - after all, the rangers didn't have enough offense in those games to get within 5 runs of the other team. and with the exception of 2002 and his slugging from 2003, his numbers in games in which they were up by 5 runs are actually substantially better. again, this isn't a big surprise, as these were games in which texas obviously had their offensive mojo working.

Sorry, but it refutes the whole study. You may be willing to bet that their numbers against middle infielders werent as gaudy, but im sure you would concede that their numbers against Texas were better than their career numbers. You also ignored the fact that they were facing, at those points in games, the worst pitchers in the sport. Until you can control for that, this is worse than meaningless. It is an irresponsible misuse of stats that will lead some people to make conclusions that are unsupported by any sort of facts.

"there are also flaws in pointing out that a-rod's numbers "were actually worse" in blow-out games, namely the fact that you're accounting for his stats for the entire game."

No, I'm not. As Yagottagotomo1 noted, the stats I listed were only his at-bats when his team was leading or behind by five runs or more.

"it's no surprise that a-rod's numbers were much worse in games where his team was trailing by 5 runs - after all, the rangers didn't have enough offense in those games to get within 5 runs of the other team."

No, Selena Roberts' point, such as it was, was that this sign-tipping was only going on in blowouts. She did not specify that it was in games the team was winning or losing - just that A-Rod was stad-padding in games that were out of reach either way.

"and with the exception of 2002 and his slugging from 2003, his numbers in games in which they were up by 5 runs are actually substantially better."

Not really. Put it this way. He had 52, 57, and 47 homers in 2001-03. In those blowout games where his team was winning by more than five runs, he had, respectively, 5 homers, 3 homers, and 1 homer. In games his team was losing by more than five runs, he had 4 homers, 2 homers, and 2 homers. Big whoop.

I don't think there would be any point in looking at individual middle infielders. When you put them all together, there are enough PAs that the aggregate is meaningful, but that's the sum of a few hundred batter-seasons. There's no way to tell which middle infielders benefited the most from the handful of PAs each individual middle infielder got.

I did not look at what A-Rod hit in blowouts because I'm not all that concerned with whether he was reciprocated, and there's not been any indication that he widely was. It would seem from your numbers that he likely wasn't widely reciprocated.

This study is not only looking at what happened in Texas. The majority of the PAs are from his time in Seattle. I didn't want to break the numbers down further into what happened with each separate team because that starts cutting the sample size below what I'm comfortable with, but I'll go ahead and do that. Breaking the numbers down into what happened in Texas and what happened in Seattle shows that the numbers went up both places, although it does look like he did it more with Texas, or at least that he was not doing it his whole career with Seattle. Obviously, if I were looking only at Texas, park and pitchers would need to be accounted for, and perhaps I should have written a bit about that rather than simply let his time in Seattle cancel some of that effect out, so I'll go ahead and do that here and give only the results from Texas.

From 2001-2003, hitter besides middle infielders increased their OPS by .080 points late in blowouts against Texas. Most, if not all, of that is probably from the park and the pitchers.

Middle infielders hitting with A-Rod at short against Texas in those years raised their OPS by .235 points. So with A-Rod at short for Texas, middle infielders raised their OPS by .155 points more than the control group. So this is definitely not a result of Texas' pitchers or park.

Sorry if this was not clear enough in the article, but the selection bias of what pitchers were in the game is accounted for by looking at a control group of how hitters (both middle infielders and all hitters) hit in these exact situations when anyone other than A-Rod is at short. Their numbers didn't go up. In fact, they went down. So this isn't a result of simply hitting better because of the game situation.

"Middle infielders hitting with A-Rod at short against Texas in those years raised their OPS by .235 points. So with A-Rod at short for Texas, middle infielders raised their OPS by .155 points more than the control group."

One minute. this is not what your numbers above show. They show that they raised their OPS in those situations by .95 points.

The numbers in the original article are the aggregate for his whole career, including Seattle as well as Texas. The numbers I just posted in my comment are only with Texas. That is why they are different.

It seems like you are asking for the exact thing I just posted, except that I'm comparing to season numbers for hitters because I think what a hitter does that season is more reflective of what he should be hitting in those PAs than what he hit for his career.

non-middle-infielders, 2001-2003, against Texas late in blowouts: +.080 OPS compared to season numbers

middle infielders, 2001-2003, with A-Rod at short late in blowouts: +.235 OPS compared to season numbers

With the Texas-only sample, 227 PAs, 214 ABs. Which is why I didn't want to split up the sample in the article. Whether he was tipping pitches in Seattle or not, it improves the study to look at them because:

1)It's unlikely he was tipping pitches simply because he was in Texas, so if he was doing it in Texas, there's a good chance he was doing it at least part of the time in Seattle too

and

2)Even if he wasn't tipping pitches at all in Seattle, the sample in Texas is too small to take at face value, and including the Seattle numbers at the very least serves to regress those numbers to the mean.

So for that reason, I would take the original numbers in the article as the better evaluation of what was gained than the numbers only in Texas, and the numbers in Texas as merely showing that the effect cannot be accounted for by looking at factors besides A-Rod (i.e. pitchers, park, etc.). The increase in OPS with A-Rod at short in Texas is big enough that it is a definite sign hitters were hitting better than they should. It's not enough to say they really hit .155 points better.

Walk rates do not seem to go up, which makes sense intuitively, since hitters are more likely to put a ball in play at some point in the at bat if they know what is coming. OBP goes up from an increase in AVG, but not nearly as much as SLG. The OPS increase is primarily from SLG (see tables in the original article for SLG/OBP breakdowns over A-Rod's career-the breakdown for just Texas is similar). You are right that if we wanted to translate this to a run-value, we would have to account for the OPS increase coming mostly from an increase in SLG rather than OBP, and that a .095 increase in OPS that is mostly SLG is not as damaging as an increase that is more OBP heavy. Since I am mostly looking for indications that A-Rod might have been tipping pitches, such as whether batters were hitting the ball better, I'm not all that concerned with assigning a run value, but your point is well-taken.

The +.080 and +.235 are how each group (non-MI and MI) hit late in blowouts compared to their season numbers. The non-MI hit .080 OPS points higher late in blowouts against Texas than their overall season numbers. The MI hit .235 OPS points higher late in blowouts against Texas (with A-Rod at short) than their overall season numbers. The MI gained .155 OPS points more late in blowouts against Texas than all other hitters gained late in blowouts against Texas.

Late in games since 2000, middle infielders have hit .023 points worse late in all 5+ run games (factoring games against Texas out of the equation will slightly drop that, but not by much). Non-MI saw about the same decrease.

This seems to go against intuition (since the pitchers are usually worse than normal), but it is probably due in part to a couple factors:

1)The batters feel less competitive in these situations and are likely slightly less focused. Pitchers, in general, may not feel the same let-down because these are pitchers who are more likely to be trying to earn more playing time or stay in the Majors, or it could be that the effect is simply more likely to affect a hitter's performance, given the relative difficulty of throwing a baseball compared to hitting one.

2)Umpires may be subconsciously more inclined to expand the zone a small amount to get the game over with once it is already more or less decided. There could be a subconscious effect of the players wanting to get the game over with and get home faster as well.

In any case, the increase seen in the study is not at all normal for what happens in the Majors in those situations.

The Yanks over 182 games with no A-Rod are a bunch of losers. Mediocre at best. You can't lose A-Rod Yankee fans. I'm sure Mark Texeira wants to lose A-Rod's protection. Look at his .187 batting average and think the Yankees are not in trouble. 2nd it's the fricking Rangers. If they were already losing running out the second best pitchers din that ball park then you know they will run up scores. This is the worse study ever by a guy who doesn't like A-Rod.

What I find fascinating is that not only did Selena Roberts not cite any stats or hard evidence to prove her game-tipping allegations, but that nobody in the mainstream media seems to be doing what we're doing - looking over the stats to see if there's anything hinky. It seems like an obvious thing to do, don't you think?

I don't think A-Rod is guilty here, for three reasons - his numbers are, for the most part, worse in blowouts. Baseball clubhouses are gossipy places - word would have leaked out long ago about this if it were the case. And finally, I just can't see Buck Showalter, the most micromanaging skipper around, not noticing A-Rod gyrating like a mime.

It does seem like the obvious thing to do. That's actually how I found the blog I linked this on where someone was asking about this very thing: I was looking for more mainstream talk about trying to look for evidence one way or the other rather than just gossiping about it or expressing personal opinions. ESPN is even a client of the Elias Sports Bureau, as well as the employer of who knows how many interns: all they have to do is ask someone to check the numbers, and it's done for them. Yet for some reason, the only thing they seem to use that for is pointless trivia or interesting bits that, while entertaining, carry little analytical value. And there's nothing wrong with those things, but why not use them for analytical purposes as well when that is also part of their business? I would assume they have access to video footage as well that they could check. I don't really get why none of the larger outlets seems to care to do any of that.

I have a different opinion on this than you, but we are both arriving at our conclusions after looking at the evidence and reasoning out what it means. That doesn't seem like so much to ask.

This is a very interesting study. My main note is this--while your sample is enough to match more than one season's worth of plate appearances for an individual player, it doesn't make any allowances for the makeup of the sample. For example, what if Derek Jeter, Nomar Garciaparra, and so on and so forth made up the larger portion of those at bats singled out by your rules, and there were fewer at bats by the lesser middle infield types, over that sample?

Mathematically, this seems to me to be a very high probability lurking variable. Publishing the players who were at the plate along with the # of ABs they contributed to the sample woudl go a long way to legitimizing your findings (and might give you reason to moderate on your conclusion).

The question I would have is how would the hitter know to look at ARod tipping the pitches? There would have to be some form of conversation out there somewhere. Spoken? E-Mail? There would have to be someone somewhere that is jealous of the ARod millions that could come forward and say he broached the subject with me, but I never accepted it. I would think a light hitting 2B somewhere would want to get back at ARod and spill his guts?

Could you look at the stats of former teammates of his to see how they did in these situations? For example look at players on his All-Star teams? Former Mariners and former Rangers? Players that are rumored to be friends of his in the off-season? Others that hung out and worked out with him and Canseco? I would think that these are the players he would have had the most contact with and would have set up agreements with him. I am no MLB player, but I did play for many years, and I can not see myself looking to see what the SS is doing before each pitch unless I knew he was going to be helping me. There has to be 1 single player somewhere that was approached and told about it, that didn't like it and will now talk about it.

Without that, all the statistical analysis in the world will not add up to a smoking gun.

I doubt there is enough data to make a real analysis - but what about the same situations against Texas in the games he was sitting on the bench or not in the game? Then you keep the same pitchers ....

What about against Texas the year before he arrived and then the year after he left?

I am down on ARod, and have been for many many years - but these allegations seem pretty far fetched without some real hard evidence.

Kincaid, what about running similar numbers during his years in new york. he's no longer a middle infielder so he shouldn't be able to participate in any exchange of tipping pitches, but his average and power are comparable or better to his years in texas. i know this wouldn't negate the disparities in his texas numbers, but it would be somewhat damning if there was a large statistical difference between his years at third base and his years at short.

I don't really know how to whittle my list down to all the players A-Rod had contact with, and when he had contact with them. Looking only at his former teammates would be a starting point, but it would cut the samples to pretty low levels. The same problem occurs with looking at games he sat in Texas. Since he didn't sit much, looking at blowout games when he was sitting won't add up to much. Instead, I prefer the approach of looking at what non-MI hit in those situations against Texas. That still keeps the same pitchers and tells you how hitters who A-Rod would not have allegedly tipped did compared the ones he might have tipped.

As for looking at the New York numbers, do you mean what A-Rod himself hit in these situations when he wasn't a middle infielder? If so, that's not really what this is looking at. I'm just looking at what opposing middle infielders hit with A-Rod at short. What the Yankees' opponents hit in these situations is already part of the control group of games when A-Rod was not at short. Looking at what A-Rod hit with New York in these situations is more along the lines of what Subway Squawkers was talking about. Since there doesn't seem to be any indication that A-Rod improved in these situations even when he was in Texas, I wouldn't expect much difference in New York.